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/sci/ - Science & Math

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7447587 No.7447587 [Reply] [Original]

>familiar with the notion of a "La Grange point" due to the old movie 2010 and my animes
>assume it's just one sweet spot between two bodies
>start browsing /sci/ more often
>look it up
>it's fucking five sweet spots and an equilateral triangle and shit

Some physicist explain me this shit. Is it due to the rotation/revolution of the two bodies? I don't even find the animation helpful. I got what wiki said about equal distance from L 4 and 5 to the two bodies but this stuff is straight Magnets to me.

>> No.7447593

I'd say it's closely related to tidal forces. Or vector sum. L4 and L5 are really hard for me to visualize, though.

>> No.7447606

>>7447587
Basically it's the points on the earths orbit where the gravitational forces are exactly equal and so cancel.

>> No.7447626

I'll try to explain this shit, english is not my first language so if something does not make sense, it's most likely because of that:

>Imagine you have 2 bodies (Sun and earth, for example), rotating one around the other
>You build a satellite and want to find an orbit around the sun where the position of the satellite would be static relative to the earth and the sun (it doesn't fall on either of them, neither escapes to oblivion, neither moves at all)
>Remember that everything is spinning (even if static relative to each other)
>There are two forces that apply to your satellite, centrifugal force = C (shit's spinning yo), and gravitational force applied by both earth (Ge) and sun (Gs)
>Now you have to find the points where all that forces cancel each other
> L3: C = Ge + Gs
> L1: C + Ge = Gs
> L2: C = Ge + Gs
> L4 and L5: Vectorial mumbo jumbo... everything cancels out and = 0

Actually is much better explained here: https://en.wikipedia.org/wiki/Lagrangian_point you lazy fuck

Also some cool unstable 3D shaped orbits can be formed around these lagrange points

>> No.7447660

Simplify the orbits to perfect circles. Now you know that for an orbit to exist, the velocity vector and the force vector must be perpendicular. The lagrange points is where this happens.

>> No.7447735

>la grange

>> No.7447796

>>7447587
https://www.youtube.com/watch?v=mxpVbU5FH0s
This video explains it quite well. Usually you'd consider the satellites force vector pointed directly at the Sun's center of mass, but because of the Earth, the net force vector is pointed slightly over to be between the Sun and Earth. At this particular angle, the point which the satellite orbits is the center of mass of the Earth-Sun system. These points are actually the only stable Lagrange points, because L1 and L2 are in their own orbits around the Sun, being slowed or sped up by Earth's additional gravity, while L3 is also only orbiting the Sun and not the SUn-Earth system.

>> No.7447937

half life 5 confirmed

>> No.7447942

>>7447735
>muh grange

>> No.7448000

>>7447587
They're spots created when one body (like the Earth) orbits another body (Like the Sun). At the Earth-Sun Lagrange points, all the forces involved cancel out to create a point where an object can hang fixed relative to the Earth.

There are three forces involved - the gravity of Sun, the gravity of the Earth, and (because everything's spinning around on circular paths) centrifugal force.

At L1, the way they cancel out is pretty obvious - centrifugal force and Earth's gravity pull out, Sun pulls in, choose the distance where these cancel out.

L2 and L3 have all the gravity pointing in, so they pick a spot where going around at the same rate as Earth gives enough centrifugal force to cancel that out.

L4 and L5 are a little harder to explain. See, the Solar System doesn't orbit around the *center* of the Sun - the Earth also pulls back on the Sun, which causes it to wobble in a circular path as well. The Solar System actually orbits around the center of mass between the Earth and the Sun. At L4 and L5, because it's equal distances between the Earth and the Sun, their gravity cancels out into a net pull directly towards the center of mass. The satellite orbits around this point, causing it to keep pace with Earth.

These are the only points where gravity and centrifugal force cancels out like this.

Any two massive bodies orbiting each other have Lagrange points like this; there's Earth-Moon Lagrange points too, for instance.

>> No.7448013

>>7448000
>The Solar System actually orbits around the center of mass between the Earth and the Sun.
It's probably more accurate to say the solar system orbits around the center of mass between Jupiter and the Sun. Also, checked.

>> No.7448022

>peace sign
illuminati confirm

>> No.7448054

>>7448013
Not really, the mass of the planets in the solar system is about 1000 times less than that of the sun alone.

>> No.7448158

>>7448054

So does the difference between this >>7448000
and this >>7448013 involve some point(s) inside the body of the sun, in any event?

>> No.7448176

>>7448158
Yeah, the Sun is so massive compared to all other bodies that the Solar System's barycenter is well within the Sun.

This isn't true for most binary star systems (where typically the barycenter is between the two bodies) or for the Earth / Moon system (Where the barycenter is just barely inside the Earth)

>> No.7448188

>>7448176
Also, Lagrange points are only true zero-net-force points in systems with only two bodies massive enough to count in a circular orbit. In the real Solar System, Lagrange points aren't perfect, so you still have to do some station-keeping to keep yourself in the right place.

Also worth a mention - L1, L2, and L3 are unstable. They're like a pencil perfectly balanced on the point: There's zero sideways force, but any deviation and it will increasingly get pulled away from equilibrium.

L4 and L5 are stable equilibria; A slight wobble away from those points results in getting pulled back to stability. This means it's much easier to just park a satellite there, if you can reach it.

>> No.7448192

so basically you're taking advantage of the center of mass of more than one body of mass?

>> No.7449552

>>7448192
wat?

>> No.7449564

>>7448188
Someone on /sci/ once told me it's impossible to be at rest at any of the points, all you can do is orbit the points, is this true or was he just talking out of his ass to win an semi-related argument?

>> No.7449579

>>7449564
You should have asked him, "relative to what?"

>> No.7449592

>>7449579
I can't remember the exact details of the thread, but the basic question was if tried to keep something at L1, could you keep it there in orbit around the sun directly between the sun and earth, assuming you had thrusters to make micro adjustions until you get it right, or would it always be unstable?

>> No.7449605

>>7447587
>the grange

>> No.7449606

>>7449592
We orbit satellites around L2 because otherwise it wouldn't be able to communicate with Earth due to solar wind. However, L4 and L5 are very stable. We can even see collections of asteroids at Jupiter's L4 and L5 points.

>> No.7449607

>>7449606
That's pretty kewl.

>> No.7449608

>>7449592
technically you can turn an unstable equilibrium point into a stable one, if you have thrusters and a way to meassure your position.

The real problem although would be the fuel needed for those thurusters, because they'd need to be constantly running

>> No.7449619

>>7449608
>because they'd need to be constantly running

Yeah that's the part I don't understand. Say after a shitton of maneuvering you are in orbit around the sun exactly at L1 (ie your COM is exactly at L1).

Why would you keep needing to expend fuel to stay in L1? I don't get it, there is no nett force from either body to accelerate you out and your angular velocity around the sun remains constant to keep you rotating around with the Earth, what do you need fuel for to counteract?

>> No.7449652

>>7449619
I think it's because the solar system isn't just Earth and the Sun. Small perturbations will occur from the other planets, and as of right now a 9 body diagram is too complex for us to account for 100%. This is why my comment here >>7448013 is relevant.

>> No.7449655
File: 7 KB, 512x384, Stability and Instability.gif [View same] [iqdb] [saucenao] [google]
7449655

>>7449619
Because there's more than three objects in the Universe.

>> No.7449659

>>7449652
>>7449655
Yes, the original only considered a 3 body system. I didn't necessarily mean our sun-earth system.

>> No.7449758

>>7449619
>there is no nett force from either body to accelerate you out and your angular velocity around the sun remains constant to keep you rotating around with the Earth, what do you need fuel for to counteract?
Stable equilibriums involve net forces working to keep you in one place, and deviations from that position result in the equilibrium driving you back to it.

Unstable equilibriums have balanced net forces, but as soon as you're away from that stable point, the forces pull you away even more. The L1 point is unstable. If you can sit PERFECTLY still on the L1 point, then you don't need to use fuel. That's not possible, though.

>> No.7449818

>>7449758
This.

Ther will always be small pertubations that won't allow you to just stand still at an unstable Point.

For example a Rocket launched from earth has a small gravitational pull on an object in point L1 but it would be still enough to pull it from that point.


The unstable Lagrange Point are still interesting, because you don't need much thrust to stay there. The thurst to stay there would only be as much as the biggest pertubation

>> No.7449882

OP here, thanks folks. Now, in the elementary earth-sun case, the /location of L3-5 is clear. Call it 150M km from the sun in the appropriate triangular spots, for discussion.

Now one question is, say you put something at Earth-Sun L1. As has actually been done, and will be done again:

https://en.wikipedia.org/wiki/Advanced_Composition_Explorer

Poking around on wiki even answered my other question about the /location/ of earth/sun L1 and L2 (~1.5M km from earth, a bit closer to earth than I expected, not-to-scale pictures notwithstanding but meh)

The question was, how does the really-quite massive and really-quite influential Venus perturb such a thing, when it orbits by over the course of an (Earth) year or two? I even searched venus in the above link and came up with nothing. Is it significant on one pass-by, or just a little meh-course correction for theoretical/actual probes?

It occurs to me that you could just as well ask how Venus "perturbs" the Earth (similar distances at closest approach), but then we're talking about comparable masses.

Looking up inner solar system orbits for this taught me just how not-eccentric Venus and Earth's are, while Mercury and Mars are quite eccentric.

>> No.7449887

>>7449655
>>7449758
>>7449818
Thanks, I understand it now.

>> No.7449889

>>7449882

And given the proximity of Earth-Sun L1 to earth (now that I know), perhaps the better question is, "how does the MOON perturb a small probe here?"